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Table5-2shows the details of a one-peak fit to the first B−O correlation inT(r). Al- though the low-x coordination numbers are reasonable, at higher x (in particular at

x = 0.6) the value is much lower than expected. Examining the residual of the fit

(Fig.5-10a) shows that the oscillations remaining are greater than those present in the short-r region preceding the first peak, indicating that a single-peak fit is inadequate. This is consistent with the presence of [BO₄] units indicated by NMR [1].

By fitting two peaks to the first B−O correlation, better fits are produced, at least in terms of the residual, as demonstrated in Figure5-10b. However, attempting to fit two peaks to the x = 0.1 and x = 0.2 samples resulted in unreasonable fits, suggesting

that the second peak, if present, is too small to be accurately modelled. Where two- peak fits were possible, average bond lengths were constrained at 1.371 Å and 1.477 Å, as calculated from bond-valence parameters [19, 20] for three- and four-coordinated

Chapter 5. Antimony Borate Glasses

Figure 5-9 The weighted total correlation function for the antimony bo- rates, obtained by dividingT(r) by the Sb−O partial correlation coefficient.

xvalues used are from the nominal batch compositions.

Table 5-2 B−O coordination numbers obtained from a one-peak fit of the first T(r) peak of the antimony borate samples; average bond lengths and RMS deviations are also given. Errors quoted are the statistical errors from fitting the peaks.

x(nominal) r_BO D u2_BOE1/2 nBO 0.1 1.371(1) 0.045(2) 2.92(5) 0.2 1.371(1) 0.049(1) 3.02(2) 0.3 1.378(1) 0.052(1) 2.96(3) 0.4 1.376(1) 0.053(1) 3.02(2) 0.5 1.380(1) 0.057(2) 2.92(5) 0.6 1.382(2) 0.057(3) 2.65(6) 0.7 1.377(1) 0.053(2) 2.83(4)

Chapter 5. Antimony Borate Glasses

Figure 5-10 The residuals of (a) single- and (b) double-peak fits to the first B−O correlation for thex=0.4 (nominal composition) antimony borate sample.

boron, respectively—it is worth noting that the earlier single-peak fit (with the bond length unconstrained) obtained the three-coordinated boron distance forx=0.1 andx=

0.2. The coordination numbers calculated from the fits are given in Table5-3. Note that the errors displayed for the totaln_BOare from single-peak fits; due to the small distortion on the greater-rside of the peak mentioned earlier, the error on the second B−O peak —and consequently, also the error on the first peak—are exaggerated. Therefore, the error from the single-peak fit is deemed to be a more realistic measure of uncertainty for the overall coordination number.

Although fitting B−O with two peaks has improved the residual, the total coordina- tion numbers obtained have not significantly changed, aside from an increased error due to the disparity in size between the two peaks fitted. Notably, the coordination number of the x = 0.6 sample is still too low: this may indicate that the composition that has

been used for the analysis is incorrect. Underestimating the proportion of Sb₂O₃in the sample would result in coordination numbers that are too low for B−O and too high for Sb−O, due to the use of inaccurate partial correlation coefficients. Since the quan- titative NMR of Holland et al. [1] (Table5-1) indicated a significantly higher x value for this sample, it seems prudent to re-examine the diffraction data using the alternate compositions, despite the discrepancies with the densities noted in§5.3.

Chapter 5. Antimony Borate Glasses

Table 5-3 B−O coordination numbers obtained from a two-peak fit of the first T(r) peak of the antimony borate samples. Also shown are calculated coordination numbers from the N₄ values provided by Holland et al. [1]. Errors quoted are the statistical errors from fitting the peaks, except for the totaln_BO, where the errors from a single-peak fit were deemed more realistic (see main text).

x(nominal) n_BO(1) n_BO(2) Totaln_BO n_BO(NMR [1])

0.1 2.92(5) – 2.92(5) 3.01(1) 0.2 3.02(2) – 3.02(2) 3.05(1) 0.3 2.66(6) 0.33(11) 2.98(3) 3.09(1) 0.4 2.76(5) 0.31(10) 3.07(2) 3.12(1) 0.5 2.52(7) 0.49(8) 3.01(5) 3.13(1) 0.6 2.26(12) 0.42(21) 2.68(6) 3.13(1) 0.7 2.59(5) 0.28(5) 2.88(4) 3.10(1)

Table 5-4 B−O coordination numbers obtained from a two-peak fit of the firstT(r) peak of the antimony borate samples, usingxvalues measured by Hollandet al.[1]. Also shown are coordination numbers calculated from the

N₄ values obtained from the same source. Errors quoted are the statistical errors from fitting the peaks, except for the totaln_BO, where the errors from a single-peak fit were deemed more realistic (see main text).

x(NMR [1]) n_BO(1) n_BO(2) Totaln_BO n_BO(NMR [1])

0.097 2.89(3) – 2.89(3) 3.01(1) 0.185 3.09(2) – 3.09(2) 3.05(1) 0.302 2.66(3) 0.37(3) 3.03(2) 3.09(1) 0.442 2.81(5) 0.29(5) 3.10(4) 3.12(1) 0.516 2.65(6) 0.44(5) 3.09(4) 3.13(1) 0.638 2.47(5) 0.50(4) 2.97(4) 3.13(1) 0.691 2.68(6) 0.30(5) 2.98(5) 3.10(1)

Table5-4 shows the parameters derived from two-peak fits to the data when anal- ysed using the NMR x values. As previously, peak positions were fixed and only a single peak could be fitted to the samples at x ≤ 0.2. With this analysis coordination

numbers are more consistent between samples, but still too imprecise to compare with those calculated from NMR. This does not necessarily indicate that the compositions are still incorrect: the relatively small variation in N4 between the samples combined

with the low number of [BO₄] units overall may simply mean that neutron diffraction is less suitable than NMR for accurately determining B−O coordination in these samples. If the compositions are still inaccurate however, this should be evident in the coordina- tion numbers obtained by fitting the first Sb−O peak.

Chapter 5. Antimony Borate Glasses

Figure 5-11 The residual of a single-peak fit to the first Sb−O correlation for thex=0.7 (nominal composition) antimony borate sample.

As with B−O, the Sb−O correlation was first fitted with a single unconstrained peak. Whilst these fits gave reasonably consistent coordination numbers (∼3.10, using nominal x values) it became apparent from the residual that a second smaller peak at greaterrwas also present (Fig.5-11): as a result, two peaks were instead fitted where possible. The two-peak fits were constrained by requirements for positive peak areas and identical RMS deviations, in order to produce sensible peaks (the second constraint is an approximation, since longer bond lengths should result in weaker bonds and higher deviations for the same pair of atoms). Table5-5shows the parameters resulting from data analysed with both nominal xvalues and those derived from NMR. Although two peaks could only be distinguished forx ≥ 0.4, the noticeable increase inr_SbO(1) for the

x=0.3 sample suggests that the second peak is still present at low x.

From these coordination numbers it is evident that some of thexvalues derived from NMR are less appropriate than the nominal compositions: for example,x= 0.44 results

in a total coordination number of 2.76(5), whereas a value of 3.00 or greater is expected, based on a network of [Sb3+O₃] trigonal pyramids with some more highly-coordinated units arising from the presence of Sb5+. It is also notable that, when using the NMR- derived compositions ofx=0.44 andx=0.64 the densities of these two samples do not

Chapter 5. Antimony Borate Glasses

Table 5-5 Sb−O coordination numbers obtained from two-peak fits of the second peak present in theT(r) of the antimony borate samples, using both nominalxvalues and those from NMR [1]. Errors quoted are the statistical errors from fitting the peaks.

x(nominal) r_SbO(1)(Å) n_SbO(1) r_SbO(2)(Å) n_SbO(2) Totaln_SbO

0.1 1.972(1) 4.73(2) – – 4.73(2) 0.2 1.978(1) 3.13(1) – – 3.13(1) 0.3 1.982(1) 3.20(1) – – 3.20(1) 0.4 1.973(1) 2.73(3) 2.086(5) 0.43(3) 3.15(7) 0.5 1.974(1) 2.86(2) 2.101(3) 0.48(2) 3.34(3) 0.6 1.978(1) 2.99(1) 2.126(3) 0.48(1) 3.46(3) 0.7 1.978(1) 2.89(1) 2.147(3) 0.32(1) 3.21(1)

x(NMR [1]) r_SbO(1)(Å) n_SbO(1) r_SbO(2)(Å) n_SbO(2) Totaln_SbO

0.097 1.973(1) 5.33(2) – – 5.33(2) 0.185 1.974(1) 3.54(2) – – 3.54(2) 0.302 1.985(1) 3.31(2) – – 3.31(2) 0.442 1.973(1) 2.36(3) 2.085(4) 0.39(2) 2.76(5) 0.516 1.971(1) 2.67(2) 2.084(3) 0.53(2) 3.20(5) 0.638 1.978(1) 2.81(2) 2.124(4) 0.45(1) 3.25(3) 0.691 1.978(1) 3.13(1) 2.152(2) 0.33(1) 3.46(1)

cases it is not evident which of the two compositions—nominal or NMR-derived—is more representative of any individual glass sample.